The transition to low carbon societies may increase peak electricity demand, which can be costly to supply with renewable energy, whose availability is uncertain. Buildings are often the main cause of peak demand, and they are believed to hold a large unrealised energy-efficiency potential. If realised, this potential could considerably mitigate the transition costs to low carbon societies, reducing average and peak electricity demands. We explore this potential in several cost-optimal global warming (GW) mitigation scenarios using a multi sector TIMES energy system model of the province of Quebec for the period 2011-2050. Heating and conservation measures in the residential sector are modelled using building simulations and parameters' values from the literature. The intra-annual availability of renewable energy and electricity imports is derived from time series analysis. Additionally, the influence of key parameters such as the projections of primary energy demand and emissions from reservoir impoundment is evaluated. Finally, we discuss some of the barriers that could hamper the energy transition and how they can be overcome. Results indicate that peak demand would rise by 30% due to GW mitigation efforts, but it can be effectively reduced by interventions in the residential sector. Heat pumps are the most cost effective heating technology, despite their lower efficiencies in cold climates. Better-insulated building envelopes have an important role in new houses, reducing by 14% the GW mitigation costs and suggesting that building codes should be more ambitious. The scenario considering denser urban developments has much lower GW mitigation costs, underscoring the importance of urban planning and potential changes in demand. The observed uptakes are contingent to the pricing of energy services being based on marginal costs and cost-optimising behaviour, and are less likely to take place with current market barriers. Finally, the emissions from reservoir creation alter the merit-order of electricity supply, favouring run-of-river power plants and suggesting that these emissions should be considered in GW mitigation scenarios.